Abstract
We propose two exact methods to solve an integrated employee-timetable and job-shop-scheduling problem. The problem is to find a minimum cost employee-timetable, where employees have different competences and work during shifts, so that the production, that corresponds to a job-shop with resource availability constraints, can be achieved. We introduce two new exact procedures: (1) a decomposition and cut generation approach and (2) a hybridization of a cut generation process with a branch and bound strategy. We also propose initial cuts that strongly improve these methods as well as a standard MIP approach. The computational performances of those methods on benchmark instances are compared to that of other methods from the literature.
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Notes
In our implementation, those variables are not created. Variables x eks are thus created if and only if the employee e can work on machine k (k∈K e ) and is available on shift s (s∈S e ).
\(\mathit {gap}=\min (1, \frac{|\mathit{value}-\varTheta ^{*}|}{\varTheta ^{*}} )\) if a solution value has been found, 1 otherwise.
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Acknowledgements
The authors wish to thank Christian Artigues for kindly giving us access to his code and test problems. Thanks are also due to the anonymous referees who provided useful comments and suggestions that led to improvements in the paper.
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All experiments have been carried out on a standard PC (Intel(R) Core(TM) i3 CPU M 370 @ 2.40 GHz, 2.39 GHz, 3.42 Go RAM) running MS Windows XP. Our own procedures are implemented in Java. The software of Artigues et al. (2009) is the original one, kindly provided by the authors, and is written in C++. Mixed integer and/or continuous linear programs have been solved with Ilog Cplex 12.2; for constraint based scheduling, we used Ilog Solver 6.7 and Scheduler 6.7.
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Guyon, O., Lemaire, P., Pinson, É. et al. Solving an integrated job-shop problem with human resource constraints. Ann Oper Res 213, 147–171 (2014). https://doi.org/10.1007/s10479-012-1132-3
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DOI: https://doi.org/10.1007/s10479-012-1132-3